B. Brügmann, University of Jena, SFB/Transregio 7 http://www.tpi.uni-jena.de
Bernd BrügmannUniversity of Jena
Kyoto, 6.6.2013
Outline: 1. Gravitational waves and the two-body problem in general relativity 2. Black hole binaries 3. Neutron star binaries
Black Hole (and Neutron Star) Binaries in Numerical Relativity
B. Brügmann, University of Jena, SFB/Transregio 7 http://www.tpi.uni-jena.de
Any non-uniform and non-spherical motion of massgenerates gravitational waves
ThorneCarnahan
aLIGO, aVirgo GEO-HFKAGRA
ET, eLISAPTA
• speed of light, long range, no shielding F_gravity = F_electric / 10^36• everyday waves are exceedingly weak → black holes, neutron stars, supernovae, big bang, ...• hard to detect, hard to block• no direct detection yet (!!)
B. Brügmann, University of Jena, SFB/Transregio 7 http://www.tpi.uni-jena.de
Gravitational wavesare a new windowinto the universe:
WHAT WILLWE SEE?
S. Rowan, GWIC
Gravitational Wave Astronomy
B. Brügmann, University of Jena, SFB/Transregio 7 http://www.tpi.uni-jena.de
Theory and Observation
Solve Einstein equations 1. theory of the sources2. templates to filter waves from noise (typically required)3. physical parameters from analysis of waves
GR eqns and GR hydro require advances in analytics, numerics, computationswell-posedness, gauge, BH singularities, microphysics, rotation, magnetic fields, ...
Observe AND UNDERSTAND what is not visible by other means:
black holes e.g. in binaries, mergers/collisions, mass censusneutron stars e.g. equation of state via oscillations, tidal dis., gamma ray burstssupernovae e.g. GW from interior of type-II, convectioncosmology e.g. big bang to within 10-24 secondsthe unknown e.g. a surprise, at least a test of relativity
GW are complementary to all other fields/particles (multi-messenger astronomy)
B. Brügmann, University of Jena, SFB/Transregio 7 http://www.tpi.uni-jena.de
Einstein Equation in Vacuum
R (g, ∂g, ∂∂g) = 0
- black holes, gravitational waves
- neutron stars etc. with stress energy tensor on right hand side
- reformulation required to obtain standard PDE evolution problem
B. Brügmann, University of Jena, SFB/Transregio 7 http://www.tpi.uni-jena.de
Numerical Relativity = Spacetime Engineering, R = 0
B. Brügmann, University of Jena, SFB/Transregio 7 http://www.tpi.uni-jena.de
Some milestones of 3d black hole evolutions
Last missing pieces of BBH puzzle: 2005: Pretorius: constraint damping (Gundlach et al) for harmonic code 2006: Campanelli, Lousto, Marronetti, Zlochower; Baker, Centrella, Choi, Koppitz, Meter: moving puncture 'gauge'
1995: Schwarzschild in 3d NCSA1999: Grazing Collision AEI, Texas/PSU2001: Plunge from ISCO AEI2004: One Orbit PSU/Jena2005: Orbit, Merger, Waves Pretorius, Brownsville, Goddard2006: Several orbits before merger2007: Kicks, Spin-Kicks2010: Rochester, Goddard, Georgia Tech, AEI, LSU, (Maryland) Caltech, Cornell, Florida Atlantic, Sperhake, Pretorius, Jena
B. Brügmann, University of Jena, SFB/Transregio 7 http://www.tpi.uni-jena.de
Parameters of Black Hole BinariesIgnore field content (waves)Ignore deformations (quasi-normal ringing)
Position: separation, varies along orbit
Mass: M = m1+m2, q = m1/m2 kicks
Momentum bound: eccentric, quasi-circular unbound: collisions, scattering
Spin spin-orbit, spin-spin coupling precession, spin-flips, hang-up/speed-up, kicks
Emission of gravitational waves accelerating inspiral precession of “orbital plane” motion of “center of mass”
m1
P1
S1
m2
P2
S2
L
B. Brügmann, University of Jena, SFB/Transregio 7 http://www.tpi.uni-jena.de
Twisted pair of pants: orbits and merger of
two black holes
event horizon (!)in x-y-t diagram
unequal massno spin
M. Thierfelder
B. Brügmann, University of Jena, SFB/Transregio 7 http://www.tpi.uni-jena.de
Orbits and merger oftwo black holes
gravitational wavesr Re(Psi4)
masses 1:1.5no spininitial d = 7M
volumeisosurfacesprojection on spherez=0 plane
min/max = 0.005box -96 to +96time step 1M
B. Brügmann, University of Jena, SFB/Transregio 7 http://www.tpi.uni-jena.de
Binary Black Hole Simulations 2007 - 2013
Mathematical, numerical,computational work
GOLD-RUSH in PARAMETER-SPACE
Gravitational wave templates including fully relativistic merger
General relativity and astrophysics of blackhole mergers
• analytic moving puncture gauge• validation: Samurai project
• templates: post-Newtonian (EOB) heuristic/hybrid templates• data analysis: NINJA, NRDA, NRAR
• kicks: unequal mass (10:1), spin kicks super-kicks of up to 4000km/s• eccentricity, zoom-whirl orbits• horizons; N-black-hole
new directions:• extreme spin, 100:1 • matter, electromagnetic counterparts• high energy black hole collisions• AdS, higher dimensions
B. Brügmann, University of Jena, SFB/Transregio 7 http://www.tpi.uni-jena.de
Binary Black Hole Simulations 2013
Mathematical, numerical,computational work
GOLD-RUSH in PARAMETER-SPACE
Gravitational wave templates including fully relativistic merger
General relativity and astrophysics of blackhole mergers
Current capability of BH-BH simulationscmp. NRAR (NINJA-2, Samurai)
• 20 GW cycles before merger (< 40)• Δφ < 0.25 radian at merger• ΔA/A < 1%• e < 0.002 (quasi-circular) • q ≤ 4 (≤ 10, max 100)• s ≤ 0.8 (approaching max spin, 'linear')
high-order finite diff. and spectral methods
B. Brügmann, University of Jena, SFB/Transregio 7 http://www.tpi.uni-jena.de
Some recent examples, BHs and NSs, Jena et al.
Mathematical, numerical,computational work
GOLD-RUSH in PARAMETER-SPACE
Gravitational wave templates including fully relativistic merger
General relativity and astrophysics of mergers
• Trumpet initial data: solving the constraints in the moving puncture gauge• Matter collapse in puncture gauge• PDE formulation: Z4c system• Spectral method
• Templates: NRDA• Accurate/long NS-NS inspirals• NS+EOB → talk by Bernuzzi
• Eccentric BH-BH orbits, zoom-whirl at intermediate momenta• Eccentric NS-NS orbits, orbit induced oscillations
B. Brügmann, University of Jena, SFB/Transregio 7 http://www.tpi.uni-jena.de
2 black holes, equal masses, no spin (numerical relativity) Müller, Gold, BB 09
B. Brügmann, University of Jena, SFB/Transregio 7 http://www.tpi.uni-jena.de
Orbital precession due to general relativity
Kepler, Newton Einstein
(BR96)
B. Brügmann, University of Jena, SFB/Transregio 7 http://www.tpi.uni-jena.de
Special/extreme eccentricity: zoom-whirl orbits
Newton: Kepler orbits, ellipses for bound orbits
Einstein: precessing ellipses, but also fine-tuned orbits in Schwarzschild and Kerr show zoom-whirl behavior
→ Easily exceed the 5% radiated energy of equal mass binaries (15-30% reported) How many whirls are possible for comparable masses? Relevance for astrophysics? High energy collisions?
Many refs on geodesics and post-Newtonian; numerical relativity:Pretorius, Khuranna 07; Healy et al 08/09;Sperhake et al 09; Gold, BB 09+12
B. Brügmann, University of Jena, SFB/Transregio 7 http://www.tpi.uni-jena.de
Zoom-whirl, equal mass/no spin, low momentum (NR) Gold, BB 12
B. Brügmann, University of Jena, SFB/Transregio 7 http://www.tpi.uni-jena.de
Puncture method for black holes
Moving puncture gauge surprisingly successful!
Analytic/geometric understanding: Wormhole puncture initial data evolves to trumpet data Hannam, Husa, Pollney, BB, O'Murchadha 2007; Brown 2008; ... Brandt, BB 1997
Basic idea: the conformal factor absorbs the coordinate singularity (pole) that encodes the black hole
B. Brügmann, University of Jena, SFB/Transregio 7 http://www.tpi.uni-jena.de
Puncture method for black holes
B. Brügmann, University of Jena, SFB/Transregio 7 http://www.tpi.uni-jena.de
Puncture method for black holes
B. Brügmann, University of Jena, SFB/Transregio 7 http://www.tpi.uni-jena.de
Puncture method for black holes
New: Solve constraints for trumpet (!) initial data Rewrite Hamiltonian constraint with ψ→1/ψ Gundermann 2010, Dietrich, BB 2012/13: 1+log trumpets, K ≠ 0 Baumgarte 2012: maximal trumpets, K = 0
B. Brügmann, University of Jena, SFB/Transregio 7 http://www.tpi.uni-jena.de
Trumpet solution from spherical gravitational collapse with puncture gauges Thierfelder, Bernuzzi, Hilditch, BB, Rezzolla 2011
B. Brügmann, University of Jena, SFB/Transregio 7 http://www.tpi.uni-jena.de
Spectral methods for black hole spacetimes
Vacuum spacetimes: smoothness of metric variables allow high order methods→ spectral methods can be optimal if applicable
Pilot projects bam → bampsBB 2013: Stability of Schwarzschild black hole in 3d spin-weighted spherical harmonics, tensor filters, GPU computingWeyhausen, Hilditch, BB (in prep 2013): 3d Nonlinear Waves
Nonlinear waves on fixed 2d background:Harms, Bernuzzi, BB 2013: Numerical solution of the 2+1 Teukolsky equation on a hyperboloidal and horizon penetrating foliation of Kerr and application to late time decays→ time domain integration→ first results on |s| = 2
B. Brügmann, University of Jena, SFB/Transregio 7 http://www.tpi.uni-jena.de
Tails for 2+1 Teukolsky equation, time domain, |s|=0,1,2Harms, Bernuzzi, BB 2012
Scri: hyperboloidal foliation, Rasz Toth 2011
Additional regularization neededfor |s| > 0, cmp. Zenginoglu 2012
Quadruple precision required
Confirms analytic calculationsby Hod 2000 (case distinctions!)
s=-2 numerical time integration, Krivan,Laguna, Papadopoulos, Andersson 1997
B. Brügmann, University of Jena, SFB/Transregio 7 http://www.tpi.uni-jena.de
Tails for 2+1 Teukolsky equation, time domain, |s|=0,1,2Harms, Bernuzzi, BB 2012
Price 1972: late time decay ∼ t -µHere: s=-2, finite | null infinity, time splitting bold, various ID→ preparatory for BH-test mass calculations (Bernuzzi, Nagar)→ extremal spin, superradiance cavity (Andersson, Glampedakis 1999, Yang et al. 2012)
B. Brügmann, University of Jena, SFB/Transregio 7 http://www.tpi.uni-jena.de
Z4c Formulation for 3d BHs and NSsHilditch, Bernuzzi, Thierfelder, Cao, Tichy, BB 2012
NS-NS
B. Brügmann, University of Jena, SFB/Transregio 7 http://www.tpi.uni-jena.de
Neutron Star Binary: long/accurate quasicircular inspiralBernuzzi, Thierfelder, BB 12
Catching up:
Simplest model: equal mass, Γ=2 polytrope, no MHD, no neutrinos …Focus on accurate simulations suitable for gravitational wave analysis
Longest and most accurate simulation of the simplest typeAlso Baiotti et al 2011, Hotokezaka et al 2013
B. Brügmann, University of Jena, SFB/Transregio 7 http://www.tpi.uni-jena.de
Neutron Star Binary: eccentric inspiralsGold, Bernuzzi, Thierfelder, BB, Pretorius 12
First simulations studying eccentricity in significant detail
Superposition of boosted TOV stars – constraints not solved (cmp. Lehner et al., new project C. Markakis, N. Moldenhauer)
Features:- Orbit Induced Oscillations Turner 1977 Newtonian; Kokkotas, Schäfer 1995 post-Newtonian- Large disk mass of about 10% of total initial mass
Compare eccentric BH-BH and BH-NS (e.g. Pretorius et al 2012, masses different)
Compare Newtonian simulations (e.g. Rosswog, Piran, Nakar 2012)
Population of eccentric NS-NS is very uncertain. Small to extremely small?
B. Brügmann, University of Jena, SFB/Transregio 7 http://www.tpi.uni-jena.de
Neutron Star Binary: eccentric inspirals induce oscillationsGold, Bernuzzi, Thierfelder, BB, Pretorius 12
Tracks for model 1, 2, 3 Waveform and instantaneous frequencyModel 3, f-mode in green
B. Brügmann, University of Jena, SFB/Transregio 7 http://www.tpi.uni-jena.de
Neutron Star Binary: eccentric inspirals induce oscillations
cmp. e.g.Kokkotas et al.
Gold, Bernuzzi, Thierfelder, BB, Pretorius 12
Model 2 and 3, rest-mass density andpower-spectral density, l=m=2, f-mode
B. Brügmann, University of Jena, SFB/Transregio 7 http://www.tpi.uni-jena.de
Gold, Bernuzzi, Thierfelder, BB, Pretorius 12Neutron Star Binary: eccentric inspirals increase disk mass
eccentricity can lead to significantly larger disk mass
B. Brügmann, University of Jena, SFB/Transregio 7 http://www.tpi.uni-jena.de
Summary
●Numerical relativity is reaching long-standing goals:●
●Insights for general relativity●Astrophysics of black holes
●and neutron stars●Gravitational wave templates
1995: Schwarzschild in 3d1999: Grazing collision2002: plunge from ISCO 2004: one orbit2006: several orbits2009: physics: spins, kicks, wave templates ...2013: more realistic matter
